Answer to Question #160023 in Real Analysis for Luna

Question

Suppose that y=f(x) is a continous function on x∈[-1,3], and f(-1)=4, f(3)=7. We can conclude that

a) there exists c∈(-1,3) such that f(c)=0

b) there exists c∈(-1,3) such that f(c)=5

c) there exists c∈(4,7) such that f(c)=0

d) there exists c∈(4,7) such that f(c)=5

e) there exists c∈(-1,1) such that f(c)=3

Answer 1

By the intermediate value theorem, we have that $\exist c \in (-1,3) \ni f(c) = 5$ . Option (b) is therefore the answer